This should do it:
<script type="text/javascript">
function getSelected(select) {
alert(select.options[select.selectedIndex].value);
}
</script>
<select id="short_code" onchange="getSelected(this)">
<option value="12">First</option>
<option value="11">Second</option>
<option value="10">Third</option>
<option value="9">Fourth</option>
</select>